JOURNAL OF REGIONAL SCIENCE, VOL. 44, NO. 3, 2004, pp. 437–466
THE SPATIAL DISTRIBUTION OF WAGES: ESTIMATING THE
HELPMAN-HANSON MODEL FOR GERMANY*
Steven Brakman
Department of Economics, University of Groningen, PO Box 800, 9700AV Groningen,
The Netherlands. E-mail: [email protected]
Harry Garretsen
Utrecht School of Economics, Utrecht University, Vredenburg 138, 3511, The
Netherlands. E-mail: [email protected]
Marc Schramm
Utrecht School of Economics, Utrecht University, Vredenburg 138, 3511, The
Netherlands. E-mail: [email protected]
ABSTRACT. Using German district data we estimate the structural parameters of a
new economic geography model as developed by Helpman (1998) and Hanson (1998,
2001a). The advantage of the Helpman-Hanson model is that it incorporates the fact
that agglomeration of economic activity increases the prices of local (nontradable) services, like housing. This model thereby provides an intuitively appealing spreading force
that allows for less extreme agglomeration patterns than predicted by the bulk of new
economic geography models. Generalizing the Helpman-Hanson model, we also analyze
the implications for the spatial distribution of wages once the assumption of real wage
equalization is dropped. If we no longer assume real wage equalization we find support
for a spatial wage structure as well as for the relevance of the structural parameters of
the theoretical model.
1.
INTRODUCTION
Krugman (1991) initiated renewed interest in mainstream economics
in recent years into how the spatial distribution of economic activity arises.
The literature on the so-called new economic geography or geographical
economics shows how modern trade and growth theory can be used to give
a sound theoretical foundation for the location of economic activity across
*We would like to thank the editors, three anonymous referees, Paul Elhorst, Michael
Funke, Michael Pflüger, Michael Roos, and seminar participants at the HWWA Hamburg,
University of Groningen, University of Amsterdam, Utrecht University, CESifo Munich,
Netherlands Bureau for Economic Policy Analysis (CPB) The Hague, and DIW Berlin for their
comments. Finally we would like to thank Dirk Stelder for his help in drawing the maps.
Received: June 2002; Revised: May 2003 and June 2003; Accepted: August 2003.
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space.1 The seminal book by Fujita, Krugman, and Venables (1999) develops and
summarizes the main elements of the new economic geography approach. The
emphasis in this book is strongly on theory, and empirical research into the new
economic geography is hardly discussed at all. As already observed by Krugman
(1998, p. 172), this is no coincidence since there is still a lack of direct testing of
the new economic geography models or their implications. In a review of Fujita,
Krugman and Venables (1999), Neary (2001) concludes that empirical research
is lagging behind and that much more work needs to be done. To make progress
an empirical validation of the main theoretical insights is necessary. The reason
that the empirical research lags behind is that the new economic geography
models are characterized by nonlinearities and multiple equilibria, and this
makes empirical validation relatively difficult.
A substantial amount of empirical research shows that location matters,
but there are still relatively few attempts to specifically estimate the structural parameters of new economic geography models (see the surveys by
Overman, Redding and Venables, 2003, and Head and Mayer, forthcoming).
A notable exception is the work by Gordon Hanson (1997, 1998, 2001a).
Hanson uses a new economic geography model developed by Helpman (1998)
and then directly tests for the significance of the model parameters. Based on
U.S. county-data, he finds confirmation for his version of the Helpman model
but the underlying demand linkages are of limited geographical scope. In this
paper we apply the Helpman-Hanson model to the case of Germany. The
contribution of the paper is threefold.
First, we want to establish whether the Helpman-Hanson model can be
verified, whether the key model parameters are significant and offer a meaningful description of the basic spatial features of an economy, in our case the
German economy. The main equation to be estimated will be a wage equation;
central to this equation is the idea that wages will be higher in those regions
that have easy access to economic centers due to stronger demand linkages.
The main geographical unit of analysis is the German city-district (kreisfreie
Stadt).
Second, we extend Hanson’s analysis by not only using housing stock but
also land prices in our model. The latter variable is more in line with the
Helpman-Hanson model, in particular, with respect to the nontradable good
(housing) that plays a key role as a spreading force in the model. Our main
extension is that we drop the assumption of real wage equalization as this may
not be very realistic for most continental European countries and especially
for reunified Germany in the mid-1990s. This requires an alternative specification of the wage equation.
1
Elsewhere, see in particular, Brakman, Garretsen and van Marrewijk (2001), we have
argued that it is more accurate to use the phrase ‘‘geographical economics’’ instead of ‘‘new
economic geography’’ because the approach basically aims at getting more geography into
economics rather than the other way around, but we stick here to the latter to avoid confusion.
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BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 439
Third, we compare our estimation results for the wage equation with two
alternatives by estimating a simple market potential function for wages as
well as a wage curve. The former encompasses a wide range of theoretical
approaches that explicitly include a role for location or distance, and as such
represents a summary of alternative explanations (see Harrigan, 2001). The
latter provides a spatial wage structure without using geography explicitly.
Still, it should be emphasized that our main aim is to estimate (and not to test)
the Helpman-Hanson model.
Even though the case of postreunification Germany is suitable for a new
economic geography approach (see Brakman and Garretsen, 1993) for an early
qualitative attempt), the goal of the present paper is not to analyze whether our
new economic geography model is the ‘‘best’’ model to analyze Germany after the
fall of the Berlin Wall in 1989. Similarly, it is also not the goal of this paper to
derive a model for the spatial distribution of wages that includes all potentially
relevant variables that have been mentioned in the literature. We merely want
to estimate a particular new economic geography model, here for the case of
Germany.2 The fall of the Berlin Wall creates a unique testing ground. A main
problem in estimating new economic geography models is whether or not the economy is in a long-run equilibrium and, if so, in which equilibrium. This problem is
reduced for the German case. We can assume that a few years into the reunification process the spatial allocation of economic activity is not an equilibrium and we
can assume a priori that versions that do not presuppose (real) spatial wage
equalization are to be preferred over specifications that do. In our paper we take
the approach recommended by Hanson (2001b) as a starting point. He concludes
his survey of the empirical literature of spatial agglomeration by stating that the
well-documented correlation of regional demand linkages with higher wages
‘‘would benefit from exploiting the well-specified structural relationships identified by theory as a basis for empirical work’’ (Hanson, 2001b, p. 271).
The paper is organized as follows. In Section 2, we visualize the idea that
geography matters in Germany by showing a few maps. We also give a first
indication of the importance of the housing prices, the most distinguishing
variable of the Helpman-Hanson model. In Section 3, we focus on the derivation of the empirical specification of the wage equation and discuss our data
set and some estimation issues. Section 4 gives the main estimation results for
the basic wage equation. In Section 5, we address the implications of dropping
the assumptions of real wage equalization. Section 6 briefly evaluates the
value-added of the new economic geography model by estimating two simple
alternative models, the market potential function and the wage curve. Section
7 concludes. We find the strongest support for a spatial wage structure and for
the relevance of the structural parameters once we no longer assume real
wage equalization. A comparison of our preferred model specification with the
2
For a similar attempt see Roos (2001).
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two alternative explanations of a spatial wage structure indicates that our
model does not outperform these other specifications.
2.
GEOGRAPHY AND GERMANY
In this section we briefly present some data to illustrate the spatial distribution of some key variables across Germany. Figures 1–3 below show that there
are indeed geographical or spatial differences within Germany with respect to
the key economic variables of our model. For example, Figure 1 gives GDP per
km2 (in millions of DM) for the 441 German districts (Kreise) that make up our
data set and shows that geographical differences with respect to GDP are quite
large (and even more skewed than GDP per capita, not shown here). The map
also indicates that GDP per km2 is higher in urban districts and typically lower
in eastern German districts.
The key equation in the Helpman-Hanson model, as will be explained in
the next section, describes the spatial nature of (nominal) wages. Figure 2
indicates that not only hourly (manufacturing) wages differ remarkably
between districts, but the map also shows that eastern Germany has lower
average wages than western Germany. The dividing line between high and
low wages identifies the former border between East and West Germany to
some extent. In the Helpman-Hanson model wages in a region are higher if
that region is part of or close to a large market, proxied by GDP. This is in line
with Figures 1 and 2 because these two maps suggest a positive correlation
between nominal wages and GDP per km2 (see also Brakman, Garretsen, and
Schramm, 2002b).
Agglomeration in new economic geography models is the result of the
combination of agglomerating and spreading forces. For instance, an important agglomerating force is the size of the market (see Figure 1). Among the
spreading forces is the demand from immobile workers in peripheral regions,
but also negative feedback in the core regions, such as congestion or the
relatively high cost of housing and other local goods. An indication for the
presence of these spreading forces in core regions is, for example, land prices.
As Figure 3 indicates, land prices in eastern Germany seem on average lower
than in western Germany, but a possible dividing line between eastern and
western Germany is somewhat less clear-cut than with respect to regional
wages. Land prices per m2 are particularly high in or close to economic
centers. Land prices can be used as a proxy for housing prices and therefore,
for prices of housing services; as will become clear in Section 3, the prices of
housing services are the spreading force in the Helpman-Hanson model.
Hence, Figures 1–3 give a first indication of the spatial distribution of the
three key variables in the theoretical model: nominal wages, the size of the
market (gross domestic product, or GDP), and prices of housing services
(proxied by land prices). Taken together these maps indicate that there is no
random distribution of economic activity across Germany and that high district wages correspond with high GDP and high land prices. Also, there seems
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BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 441
to be a clustering of the three district variables. Districts with relatively high
wages, high GDP, and high land prices are typically surrounded by similar
districts, and the same holds for low-wage districts. In our estimations we
intend to determine if indeed such a regional (wage) gradient exists, as predicted by the Helpman-Hanson model.
GDP per km2
1
2
3
4–5
6–9
10–26
27–65
66–360
FIGURE 1: GDP per km2 (in Millions of DM, 1994).
Source: Federal Statistical Office, Wiesbaden.
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Missing Value
24–32
33–38
39–44
45–49
50–53
54–60
61–69
70–234
FIGURE 2: Average Hourly Manufacturing Wage (DM, 1995).
No. observations ¼ 432. Data on wages in the districts Alzey-Worms, Aurich, Emden, Gifhorn,
Landau in der Pfalz, Mainz-Bingen, Neustadt an der Weinstraße, Suedliche Weinstraße,
Wolfsburg are missing (see the shaded areas on the map)
Source: Federal Statistical Office, Wiesbaden.
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BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 443
Price of land per m2
Missing value
2–33
34–41
42–58
59–81
82–125
126–202
203–327
328–1420
FIGURE 3: Land Prices per m2 (in DM, 1995).
No. Observations ¼ 433. Data on land prices in districts Amberg (city district), Bremen, Bremerhaven,
Hamburg, Hersfeld-Rotenburg, Kassel (city district), Offenbach, Potsdam, Regensburg (city district)
and Rheingau-Taunus-kreis and are missing (these are shaded in the map).
Source: Federal Statistical Office, Wiesbaden
The inclusion of housing services as a nontradable consumption good lies
at the very heart of the Helpman (1998) model, and to illustrate that prices of
housing services may indeed display a spatial structure, as suggested by
Figure 3, we estimate a market potential function, Equation (1)
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ð1Þ
JOURNAL OF REGIONAL SCIENCE, VOL. 44, NO. 3, 2004
log ðLPr Þ ¼ k1 log½Ss Ys ek2Drs þ k3 EG þ k4 Drural þ constant
where LP ¼ land prices per m2 in district r in 1995, Y ¼ GDP in district r in
1994, Drs ¼ distance between districts r and s, EG and Drural are two dummy
variables for eastern German and rural districts, respectively; if district r is in
eastern Germany EG ¼ 1 and if district r is not a city-district, then Drural ¼ 1;
k1 k4 are coefficients to be estimated. For more details on the data see
Section 3.
The estimation results (Table 1) show that there is a ‘‘spatial land price’’
structure (k1 > 0 and k2 > 0), which means that land prices in district r are
higher if this district is near to districts with a high GDP. This is precisely
what drives the Helpman-Hanson model. Also in line with other German
evidence (see Sinn, 2000) is that land prices are significantly lower in rural
districts, but notably also in East German districts.
3.
THE MODEL AND DATA
The Helpman-Hanson Model
The benchmark model of the new economic geography, developed by
Krugman (1991), is in general not suited for empirical validation. In the long
run, the model produces only one or at most a very few equally sized locations
with manufacturing economic activity for an intermediate range of trade
costs. This is clearly not in accordance with the spatial distribution of manufacturing activity for the United States or any other industrialized country
because in reality we observe the coexistence of large and small locations.
Furthermore, it lacks some of the spatial characteristics of agglomerations
that have been found to be very relevant empirically, most importantly the
tendency of prices of local (nontradable) goods to be higher in agglomerations
(see for example the survey by Anas, Arnott, and Small, 1998, and our Figure 3
for that matter).
TABLE 1: Spatial Land Price Structure
k1
k2
k3
k4
Adjusted R2
0.408
(6.8)
0.063
(3.8)
0.586
(4.1)
1.361
(10.5)
0.726
# obs. ¼ 146, estimation method: weighted least squares (WLS), result for constant not
reported, t-statistic in parentheses.
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BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 445
Given the observation that complete agglomeration is not in accordance
with the facts, there are two alternatives. First, there are the new economic
geography models based on forward and backward linkages with no interregional labor mobility (Krugman and Venables, 1995, 1996, and Venables,
1996). However, direct testing of these models is rather cumbersome because
it requires detailed information about input–output linkages between firms on
a regional level (see Combes and Lafourcade, 2001, for an empirical test of this
class of models). Second, there is the Helpman-Hanson model, which combines
the ‘‘best of the two worlds.’’ It shares with Krugman (1991) the emphasis on
demand linkages (which are easier to test for than input–output linkages) and
at the same time, through the inclusion of a nontradable consumption good
(i.e., housing services), is capable of producing similar equilibria as the models
based on input–output linkages and immobile factors of production. The price
of housing services in the Helpman (1998) model, which increases with
agglomeration, serves as an analogous spreading force as the rising wages in
Puga (1999), for instance. In fact, it can be shown that in terms of equilibrium
outcomes the Helpman model yields similar results as the model in Krugman
and Venables (1996), where there is no interregional labor mobility and the
possibility of agglomeration arises through intricate input–output linkages
between firms.3
We briefly discuss the theoretical approach in Hanson (1998, 2001a) and
focus on the equilibrium conditions because these are needed to arrive at
the basic wage equation that will be estimated.4 With a few exceptions (notably,
the inclusion of a nontradable good: housing services) the microfoundation for
the behavior of the individual consumers and producers is the same as in the
seminal Krugman (1991) model. Since these basic features of the new economic
geography are by now well-known, we discuss only the resulting equilibrium conditions and for the full model specification we refer to Hanson
(1998, 1999). In the model, consumers derive utility from consuming a manufacturing good, which is tradable, albeit at a cost, and from housing services,
which is a nontradable good between regions. The manufacturing good consists of many varieties and each firm offers one variety; this is modeled with
the well-known Dixit-Stiglitz formulation of monopolistic competition. The
only factor input into the model is labor, which is needed to produce the
manufacturing good and can move between regions in the long run. In this
set-up of the model the perfectly competitive housing sector serves as the
3
For a discussion on differences between Krugman (1991) and Helpman (1998), see
Helpman (1998, pp. 49–53). For a very useful general framework to understand the different
implications of models with and without interregional labor mobility see Puga (1999, 2001). For
the observation that the Helpman model is analytically similar to the input-output models, see
Puga (1999, p. 324), Puga (2002, p. 388), Ottaviano and Thisse (2001, p. 175).
4
For an in-depth analysis of the Krugman (1991) model see Fujita, Krugman, and Venables
(1999, chaps. 4 and 5) or Brakman, Garretsen, and van Marrewijk (2001, chaps 3 and 4). For the
full specification of the Helpman-Hanson model, see Hanson (1998, pp. 9–12).
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spreading force because housing services (a nontradable good) are relatively
more expensive in the centers of production where demand for housing is high.
As we will see below, apart from the inclusion of a homogenous nontradable
good (housing services) at the expense of a homogenous tradable good (agriculture), there are no fundamental differences in the model set-up between
Krugman (1991) and Helpman (1998). In particular, in both models agglomeration is driven by the demand linkages and the interregional mobility of labor.
Note, however, that the comparative statics of the two models differ, notably
with respect to the implications of a change in transportation costs for the
degree of agglomeration.5 In Section 4 we will address this issue in our
discussion of the so called ‘‘no black hole’’ condition.6
This extension of the core model with a nontradable good, housing
services, thus allows for a richer menu of equilibrium spatial distributions
of economic activity than the core model. As trade or transportation costs
fall, agglomeration remains a possible outcome but (renewed) spreading and
partial agglomeration are feasible. Partial agglomeration means that all
regions have at least some industry. Notwithstanding the different implications of Helpman (1998) compared to Krugman (1991) the equilibrium conditions (five in total) are very similar to the core model; in particular, the
equilibrium wage equation, which is central to the empirical analysis, is
identical to the (normalized) equilibrium wage equation in Krugman
(1991)—see Appendix A for a derivation of equilibrium wage Equation (2)
hX
i1=e
e1 Drs ð1eÞ
Wr ¼
ð2Þ
Y
I
T
s
s
s
ð3Þ
Ir ¼
ð4Þ
hX
D 1e 1e i1=ð1eÞ
l
T rs
Ws
s
s
Yr ¼ lr LWr
in which in Equation (2) Wr is region r’s (nominal) wage rate, Y is income, I is
the price index for manufactured goods, e is the elasticity of substitution for
manufactured goods, T is the transport cost parameter, and Trs ¼ TDrs, where
Drs is the distance between locations r and s. Transport costs T are defined as
the number of manufactured goods that have to be shipped to ensure that one
unit arrives over one unit of distance. Given the elasticity of substitution e
(e > 1), it can directly be seen from Equation (2) that for every region wages are
higher when demand in surrounding markets (Ys) is higher (including its own
market), when access to those markets is better (lower transport costs T).
5
In Krugman (1991) low (high) transportation costs lead to agglomeration (dispersion),
whereas in Helpman (1998) it is the other way around.
6
This condition determines whether or not transport costs matter. If the condition is not
met, agglomeration always occurs, irrespective of transport costs.
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BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 447
Also, regional wages are higher when there is less competition for the
varieties the region wants to sell in those markets; this is the extent of
competition effect, measured by the price index Is. As to the way in which
this competition effect works, the price index Is does not measure a competition effect in the sense in which this term is normally used (price mark-ups
are fixed and there is no strategic interaction between firms). A low price
index reflects that many varieties are produced in nearby regions and are
therefore not subject to high transportation costs and this reduces the level of
demand for local manufacturing varieties. Since firms’ output level and price
mark-ups are fixed, this has to be offset by lower wages. Hence, a low (high)
price index Is depresses (stimulates) regional wages Wr.
Equation (3) gives the equilibrium price index for region r, where this
price index is higher if a region has to import a relatively larger part of its
manufactured goods from more distant regions. Note that the price index I
depends on the wages W. Equation (4) simply states income in region r, Yr, has
to equal the labor income earned in that region, where lr is region r’s share of
the total manufacturing labor force L.7
The main aim of our empirical research is to find out whether or not a
spatial wage structure, that is, a spatial distribution of wages in line with
Equation (2), exists for Germany. Equation (2) cannot be directly estimated
because there are typically no time-series of local price indices for manufactures (where local refers to the U.S. county level in Hanson’s study and to the
city-district level in our case). And, even more problematic—see Equation
(3)—the price index I is endogenous, and inter alia depends on each of the
local wage rates, which makes a reduced form of Equations (2) and (3) extremely
lengthy and complex. These problems have to be solved somehow to estimate
a spatial wage structure for Germany.
Hanson uses the following estimation strategy based on the remaining
two equilibrium conditions. In order to arrive at a wage equation that can
actually be estimated he rewrites the price index I in exogenous variables that
can actually be observed for his sample of U.S. counties.
First, he uses
ð5Þ
Pr Hr ¼ ð1 dÞYr
Equation (5) states that the market value of the housing services supplied
equals the share of income spent on housing services, where Pr is the price of
housing services in region r, Hr is the fixed stock of housing in region r, which
determines the total of housing services supplied, (1 d) is the share of income
7
Note that the housing stock is owned by absentee landlords. No income is gained from
owning houses. Dropping this assumption (by endowing each worker with a share of the housing
stock) has no impact on the empirical specifications [Equation (7)]; compare Hanson (1998) with
Hanson (2001a).
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spent on housing services, and d is thus the share of income spent on manufactures.8
Second, real wage equalization between regions is assumed
ð6Þ
d
1d d
Wr =P1d
r Ir ¼ Ws =Ps Is
Equation (6) is quite important. In fact, it is assumed that the economy has
reached a long-run equilibrium in which real wages are identical. This implies
that labor has no incentive to migrate (interregional labor mobility is solely a
function of interregional real wage differences).9 The assumption of interregional labor mobility and the notion that agglomeration leads to interregional
wage differences are not undisputed for a country like Germany with an
allegedly ‘‘rigid’’ labor market (see in particular Puga, 2002, p. 389). We return
to this issue in Section 5 where we will drop the assumption of real wage
equalization.
The importance of nontradable housing services as a spreading force is
implied by Equation (6). A higher income Ys implies, ceteris paribus, higher
wages in region r—see Equation (2)—but it also, given the stock of housing,
puts an upward pressure on the price of housing services Pr, Equation (5).
Combining Equations (5) and (6) allows us to rewrite the price index in terms
of the housing stock, income, and nominal wages. First, we rewrite (6) as
ð60 Þ
d
Wr =P1d
r Ir ¼ o
is the real wage that is assumed to be constant and identical for all
where o
regions.
Second, the equilibrium condition for the market for housing services can
be written as Pr ¼ (1 d)Yr/Hr and this expression can be substituted for Pr
into Equation (60 ); this gives the price index Ir in terms of Wr, Yr, and Hr.
Substituting this in (1) results in a wage equation which can be estimated.
This will also be the benchmark wage equation in our empirical analysis10
X
eþð1eÞ=d ð1dÞðe1Þ=d ðe1Þ=d ð1eÞDrs
ð7Þ logðWr Þ ¼ k0 þ e1 log
Y
H
W
T
þ errr
s
s
s s
where k0 is a parameter and errr is the error term. Equation (7) includes
the three central structural parameters of the model, namely share of income
spent on manufactures d, the substitution elasticity e, and the transport costs T.
8
Note that direct observation of a price index of housing services would imply that one only
has to use Equation (6) and that the use of Equation (5) is no longer necessary. We will return to
this in Section 4.
9
Overman, Redding, and Venables (2001, p. 17) and Head and Mayer (2003) discuss how the
model used by Hanson can be seen as a specific version of a more general new economic geography
model.
10
Note that this equation resembles the spatial lag model of Anselin and Hudak (1992),
although that model is linear whereas Equation (7) is nonlinear.
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BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 449
Given the availability of data on wages, income, the housing stock, and a
proxy for distance, Equation (7) can be estimated. The dependent variable is
the wage rate measured at the U.S. county level and Hanson finds strong
confirmation for the underlying model to the extent that the three structural
parameters are significant and have the expected sign which, in terms of
Equation (7), means that that there is a spatial wage structure. In Section 4
we will begin our empirical inquiry of the German case by estimating Equation (7) for our sample of German districts.
Data and Estimation Issues
Before we turn to the estimation results, a few words on the construction
of our data set are in order. Germany is administratively divided into
441 districts (Kreise). Of these districts a total of 119 districts are so called
city-districts (kreisfreie Stadt), in which the district corresponds with a city,
and 114 of these city-districts are included in the sample. We use district
statistics provided by the regional statistical offices in Germany. The data
set contains local variables such as the value-added of all sectors in that
district (GDP, our Ys variable), the wage bill, and the number of hours of
labor in firms with 20 or more employees in the mining and manufacturing
sector. Combining the latter two variables gives the average hourly wage in
the manufacturing and mining sector, regional wage Wr. Since we also want to
analyze the cities’ Hinterland we also included 37 aggregated (rural) districts,
constructed from a larger sample of 322 districts.11 The total number of
districts in our sample is thus 151, namely 114 city-districts and 37 rural
districts. Transportation costs are, of course, a crucial variable. We do not use
the geodesic distance between districts because this measure does not distinguish between highways and secondary roads. Instead, distance is measured
by the average car travel time (in minutes) from district A to district B. The
data are obtained from the Route Planner 2000.
For the data on the housing stock Hs, which are required to estimate
Equation (7), we use the number of rooms in residential dwellings per district.
As a proxy for Ps, the average land price (Baulandpreis) is used. In our
estimations we also include the following district variables to control for
location-specific fixed effects: the employment structure (the respective shares
for each district in agricultural, industrial, services and trade, and transport
employment) and two variables indicating the skill level (proportion of workers that did not complete vocational training and proportion of workers that
completed higher education/vocational training).
11
From a total of 441 districts, 322 districts do not correspond with a city. Each of these 322
districts comprise several villages and towns. In order to simplify the distance matrix considerably
we aggregated these 322 districts at the higher level of Bezirke. This leads to 37 rural districts.
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Since we only have one observation for each variable per district for the
average hourly wage and for GDP (for 1995 and 1994 respectively), we have to
estimate the wage Equation (7) in levels and we therefore restrict ourselves to
cross-section estimations. The estimation of an equation like Equation (7) raises
several estimation issues. First, there is the issue of the endogeneity of particular right-hand-side variables like Ys. In our case this problem is somewhat
reduced by the fact that wage data are for 1995 and GDP data are for 1994 (and
thus precede the wage data). However, this still leaves the local wage-rate
itself as an endogenous variable—see Ws in Equation (7). To check for this we
have experimented with instrumental variables (IV) with respect to Ws in our
estimations (not shown here, but available upon request). We used as instruments (inter alia) the size of districts, the size of the district’s population, and
the population density as instruments. The main conclusion is that these
IV-estimations do not lead to different results.
Second, if we were able to use multiple years of observation for each
variable in estimating Equation (7), the time-series element of the data
would allow us, as in Hanson’s work, to estimate in first differences. Estimation in first differences would allow us to deal with time-invariant, districtspecific effects that may have a bearing on district-wages. This is not possible
in our cross-section setting. As a next best strategy to deal with the possibility
of time-invariant location-specific fixed effects, we incorporate a number of
district variables, in particular, the skill level and the employment structure.
These and a few other variables (discussed later) are used as controls for the
presence of district or region specific determinants of wages Wr.
Third, with respect to the geographical unit of analysis, the left- and
right-hand-side variables are measured at the district level in our estimations.
In Hanson (1998) or Roos (2001) the latter are measured at a higher level of
aggregation (e.g., the U.S. state and German state [Bundesland] level [NUTS 1])
to make it less likely that a shock to district wages Wr has an impact on Ys or
Ws. On the other hand, a lower level of geographical aggregation of the data
makes it less likely that location-specific shocks—via the error-term in Equation (7)—have an impact on the independent variables.12
Finally, and related to this last observation, is the possibility that the
variance of the error-term systematically varies across the various districts.
To address the issue of heteroskedasticity we apply the Glejser-test and use
weighted least squares (WLS) estimations. Therefore, we estimate (via nonlinear least squares, NLS) Equation (7) or any other of our specifications and
then we regress the (absolute of the) resulting residuals on the right-hand-side
12
In Hanson (2001a, pp. 15–16) a different aggregation scheme is used. For each U.S.
county (the most disaggregated level of geographical analysis), surrounding counties are
grouped within concentric distance bands (up to a distance of a 1,000 km. these bands have a
width of 100 km.) and then the independent variables Ys and Ws are aggregated across the
counties within each band.
# Blackwell Publishing, Inc. 2004.
BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 451
variables. A significant impact of these variables on the residuals indicates
heteroskedasticity and for every specification it turns out that this is indeed
something that has to be taken into account. To deal with this we use weighted
least squares (WLS) estimations where the weights are for each specification
taken from the estimation results from regressing the absolute residuals (from
the ‘‘unweighted’’ NLS estimation) on the right-hand-side variables.
4.
BASIC ESTIMATION RESULTS FOR GERMANY
We now turn to the estimates of the structural parameters using the wage
Equation (7) for Germany. In doing so, we will not only be able to estimate the
structural parameters d, e, and T (and to establish the existence of a spatial
wage structure), but also to verify the so-called no-black hole condition, which
gives an indication for the convergence prospects in Germany. We first present the regression results of Equation (7), which incorporates the assumption
that the local housing stock H and GDP determine the local price of housing
services. We then present the results of the wage Equation (70 ), in which the
local land price LP is used as an explanatory variable, and where the housing
stock H is omitted. Local land prices are considered as a proxy for the local
prices of housing services P of the theoretical model, which makes Equation
(5), the equilibrium condition for the market of housing services, redundant.
To arrive at Equation (70 ) use Equation (6) to express the price index I in terms
of wages W and prices of housing services P and substitute this expression in
wage Equation (1)
X
ð1dÞð1eÞ=d ðe1Þ=d ð1eÞDrs
logðWr Þ ¼ k00 þ e1 log
ð70 Þ
Y
LP
W
T
þ errr
s
s
s s
where LP is land price.
Table 3 gives the basic estimation results for the estimation of Equations
(7) and (70 ). We also included a dummy variable for eastern German districts
and a dummy variable for rural districts.13 The dummy for eastern German
districts is motivated by the fact that wages (and labor productivity) in eastern
Germany are lower than in western Germany.14 For example, in 1995 average
labor productivity in the east’s mining sector was 68.3 percent of the level
13
Inspection of the wage data revealed that there is one very large outlier, the city of
Erlangen (Bavaria), which is the city referred to as the German capital of the pharmaceutical
industry and the city in which the Siemens company has its headquarters. Erlangen has by far the
highest wage, so we included a dummy for this district as well.
14
In our estimations we consider Germany to be a closed economy; elsewhere (see Brakman,
Garretsen, and Schramm, 2000) we have checked whether the inclusion of Germany’s main
trading partners would influence the outcomes but this was not the case. We did not control for
fixed regional endowments like climate. Hanson (2001a) does control for these endowments in his
study for the United States but for a relatively small country like Germany these kind of
differences are assumed not to be relevant.
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in the west and in the manufacturing sector it just reached 55.1 percent
(Federal Statistical Office, Wiesbaden). Furthermore, especially in East
Germany, the central wage bargaining system in Germany prevents prices
from performing their allocational role, hindering the transition process
toward a well-functioning market economy. The inflexibility of the labor
market has often been blamed for the present difficulties of the German
economy. Besides the inclusion of the dummy variables for East German
and rural districts we also included six district-specific variables as control
variables to control for location-specific effects on wages in all our estimations
in Sections 4, 5, and 6. Table 2 gives summary statistics on the district-specific
control variables (the standard deviation is a measure of the differences
between districts).
In the estimations we make sure that the share variables do not sum to
one, and are not perfectly collinear. With respect to the employment variable,
public sector employment is excluded; with respect to vocational training, we
excluded all forms of vocational training except intermediate education.
From the remaining six variables the first two pertain to the skill level
(proportion of workers that did not complete vocational training, proportion of
workers that completed higher education/vocational training). The other four
district variables pertain to the employment structure (the respective shares
for each district in agricultural, industrial, services and trade, and transport
employment). Note that, given the fact that we use WLS, the adjusted R2 is
less informative. The corresponding NLS estimations (not shown) invariably
resulted in an adjusted R2 in the range of 0.5 to 0.8.
In discussing our results the role of the eastern German EG dummy
turns out to be quite important, which explains the set-up of Table 3. First
look at columns 1 and 2 in Table 3. For the estimation of Equation (7) without
the EG dummy (see column 1), all three structural parameters are found to be
significant. They also have the correct sign, thereby validating the HelpmanHanson model. The substitution elasticity e is significant and the coefficient
implies a profit margin of 38 percent [given that e/(e 1) is the mark-up],
TABLE 2: District-Specific Control Variables (Cross-Section of 151 German
Districts) Measured in Shares of Total Employment
Vocational Training (1998)
No
West German average .203
(.029)
East German average .105
(.014)
Intermediate
High
.636
(.039)
.695
(.051)
.075
(.035)
.105
(.040)
Unweighted standard deviation in parentheses;
*Trade, transport, and communication.
# Blackwell Publishing, Inc. 2004.
Sectoral Employment (1995)
Agriculture Industry Services Other Public
(Ttc)* Services Sector
.028
(.025)
.035
(.026)
.347
(.091)
.350
(.076)
.198
(.037)
.175
(.021)
.225
.202
(.051) (.071)
.204
.236
(.040) (.063)
BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 453
TABLE 3: Estimation Results for the Bench-Mark Wage Equation
(I), Eq.(7) with
Housing Stock
and No EG Dummy,
(Number of
Observations: 151)
(II), Eq(7) with
Housing Stock and EG
Dummy (Number of
Observations: 151)
(III), Eq. (70 ), with
Land Prices and
No EG Dummy,
(Number of
Observations: 146)
d
e
Log(T)
1.333 (3.0)
3.623 (9.2)
0.007 (8.2)
12.801 (0.1)
3.105 (1.9)
0.001 (.2.0)
0.684 (28.4)
4.213 (15.9)
0.010 (10.2)
EG
Drural
Industry
Other services
Low-skilled
High-skilled
Adjusted R2
District-Specific
–
.056 (1.4)
.031 (.1)
1.165 (2.4)
.386 (.8)
2.840 (4.2)
0.99
Implied values:
e/(e 1)
e(1 d)
1.38
1.21 (1.3)*
Control Variables (dummies)
.781 (12.2)
–
.029 (.9)
.128 (2.9)
1.235 (5.6)
.494 (1.7)
1.738 (4.6)
.409 (.8)
.686 (1.3)
.228 (.4)
6.087 (10.8)
2.316 (3.3)
0.99
0.99
1.48
36.64 (0.1)*
1.31
1.33 (2.5)*
(IV), Eq. (70 ) with
Land Prices and
EG Dummy,
(Number of
Observations: 146)
0.536 (12.0)
4.987 (6.6)
0.001 (4.6)
.811
.024
1.434
1.873
1.286
6.238
0.99
(12.1)
(.6)
(6.3)
(4.8)
(2.1)
(11.0)
1.25
2.31 (4.5)*
Estimation method: weighted least squares (WLS); results for the constants, the dummy for
the city of Erlangen are not reported, as well as the result for the dummy for Hamburg in (70 );
t-statistic in parentheses; *H0: e(1 d) ¼ 1. The District specific variables, Agriculture, and Trade,
Transport, and Communication were insignificant, and are not reported.
which is fairly reasonable, although higher than found for the United States
by Hanson (1998, 2001a).15 Note that the value e(1 d) is used to determine
whether a reduction of transport costs affects spatial agglomeration of economic activity; the so called no black hole condition for the Helpman (1998)
model holds if e(1 d) < 1 (see below).16 The coefficient for d is, however,
implausibly large in the wage equation with the housing stock because it
would indicate that Germans do not spend any part of their income on housing
services—see Equation (5). Including a dummy for EG districts (column 2)
changes these results in an important way; the transportation cost coefficient
now has the wrong sign, and d becomes statistically insignificant. So, estimating Equation (7) for reunified Germany yields two problems: (i) we find d to be
(too) large, (ii) taking into account an EG dummy, because we expect for the
15
Estimates of the margin of price over marginal costs in industry are ranging from 14
percent in the United States (Norrbin, 1993), 100 percent in the United Kingdom (Haskel, Martin
& Small, 1995), to more than 100 percent in the United States (Hall, 1988).
16
In Krugman (1991) the no black hole condition is met if e(1 d) > 1. Helpman (1998) shows
that this difference is ultimately due to the fact that the spreading force in the Krugman model is
a homogeneous tradable good (the agricultural good) whereas in the Helpman model it is a
homogeneous non-tradable good (housing services which are in fixed supply).
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mid-1990s wages in eastern Germany to be lower than in western Germany,
does imply that we no longer find a spatial wage structure. One way to remedy
these problems might be to dismiss the housing stock as the preferred variable
to capture the spreading force of the nontradable service (see below). Note that
the high value found for d is, however, not at odds with the findings of Hanson,
who also finds that d is large for the United States (above 0.9).17 Finally, with
respect to the control variables it turns out that not only the EG dummy is
highly significant, but also the district-specific share of workers with a higher
education contributes quite strongly to the explanation of spatial wages.
The first column of Table 3 also shows whether or not the no black hole
condition is met. It is indeed the case that e(1 d) < 1, although not significantly (except for the case in which d is fixed; see however footnote 16). This
implies that agglomeration is not inevitable if transportation costs can be
sufficiently reduced. For Germany this seems to indicate that a lowering of
transportation costs might lead to more even spreading of economic activity,
which is good news for the peripheral districts, the bulk of which are located in
eastern Germany. In the Helpman-Hanson model e(1 d) > 1 means that a
region’s share of manufacturing production is a function of its (fixed) relative
housing stock only (Helpman, 1998, p. 40). However, the relevance of this
conclusion with respect to the no black hole condition is rather limited because
specification (7) more or less breaks down when we take into account that
the eastern German economy is rather different from its western German
counterpart (column 2).
One way to remedy the two problems in estimating Equation (7) might be
to dismiss the housing stock as the preferred variable to capture the spreading
force of the nontradable service, housing. Columns 3 and 4 in Table 3 are
therefore based on Equation (70 ), the wage equation with land prices
(Baulandpreise) as an explanatory variable instead of the housing stock.
From Table 1 we already know that land prices are higher in districts near
districts with a high GDP. A priori, estimation of the wage equation with these
price data is preferred because it provides a more direct test of the HelpmanHanson model; the influence of agglomeration on prices of local nontradables
is determining the strength of the spreading force in the Helpman-Hanson
model. Also note that by using a proxy for the Ps variable we no longer need
Equation (5), the equilibrium condition for the housing market. However, we
still need Equation (6) that assumes real wage equalization.
Column 3 of Table 3 gives the estimation results with land prices for
146 districts, excluding the dummy for EG districts. The three structural
17
Restricting d to actual values of the share of income spent on nontradable services
(or nontradable housing services) has virtually no impact on the estimated size and significance
of the transport costs T, or on the explanatory power of the estimated equation, which is still able
to explain 46 percent of the variance in wages, as compared to 48 percent in the unrestricted
specification. A likelihood ratio test indicates that the restricted model has to be rejected as being
inferior compared to the unrestricted model.
# Blackwell Publishing, Inc. 2004.
BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 455
parameters are significant with the correct sign. The most important
difference with the previous estimations with the housing stock is that the
d-coefficient is now significantly smaller than 1 which indicates that a significant part of income (1 0.684) is indeed spent on housing services and that
the housing sector can indeed act as a spreading force (the estimated share of
income spent on manufactures in Germany of 0.684 is in line with the actual
share of 0.68). This finding gives some support to the use of land prices instead
of the housing stock. Another difference is that the no black hole condition is
no longer met [e(1 d) ¼ 1.30 > 1]. This implies that the spatial distribution of
economic activity (and hence of district wages) depends only on the (fixed)
distribution of the housing stock and that it would not depend on the level of
transportation costs at all. More importantly though is that the estimation
results for Equation (70 ) with land prices and the EG dummy again yields a
wrong sign for the transportation cost parameter.
Estimating the Helpman-Hanson model for Germany by means of wage
Equations (7) and (70 ) thus leads to two conclusions. First, including land
prices instead of the housing stock is a more direct test of the HelpmanHanson model and modestly improves the estimates in the sense that the
share of spending on housing is no longer zero and is more in line with the
actual share of spending on housing. The second and more important conclusion, however, is that the model should be amended because incorporating an
outstanding feature of the reunified German Economy in 1994/1995, that is,
the inclusion of the EG dummy, gives the transportation cost parameter the
wrong sign. The most obvious amendment in the German case is to drop the
assumption of (real) wage equalization. So, what happens when we, along
with the housing Equation (5), no longer use Equation (6) to estimate our
wage equation for Germany?
5.
REAL WAGE DIFFERENCES
The assumption of real wage equalization—recall equation (6)—boils
down to imposing a long-run equilibrium and this implies a sufficient degree
of labor mobility and wage flexibility. In general, the requirement that interregional real wages are equal by assumption is not very appealing because it
implies that the economy is in a long-run equilibrium. Furthermore, and
supported by our findings in the previous section, this assumption seems at
odds with the stylized fact that (real) wages were different between eastern
and western German regions at the start of the reunification process. Another
problem with the application of wage Equation (7) to a European economy like
Germany is that the actual degree of real wage flexibility may be too low to
bring about real wage equalization.
In this section we estimate a wage equation and the structural parameters without invoking real wage equalization and thereby extend Hanson’s
(2001a) analysis. We do so by deriving a wage equation that is based on a
reduced form of the equilibrium wage Equation (2) and the equilibrium price
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JOURNAL OF REGIONAL SCIENCE, VOL. 44, NO. 3, 2004
index Equation (3). For this purpose we simplify the price index as defined in
Equation (3). For each district we focus on two prices: the price in district r of a
manufactured good produced in district r and the average price outside district
r of a manufactured good produced outside district r. The determination of the
simplified local price index for manufactures requires a measure of average
distance between region r and the regions outside. The distance from the
economic center is an appropriate measure in our view. This center is obtained
by weighing the distances with relative Y.18 The economic center of Germany
turns out to be Landkreis Giessen (near Frankfurt), which is in the state of
Hessen, West Germany. Equation (3) now becomes
h
1e i1=1e
Ir ¼ lr Wr1e þ ð1 lr Þ W r T Drcenter
ð30 Þ
where W r is the average wage outside district r, Dr-center is the distance from
district r to the economic center, and weight lr is district r’s share of employment in manufacturing, which is proportional to the number of varieties
of manufactures. This simplified price index makes it possible to directly
estimate the wage equation.
However, as in Section 4, we also want to take into account that labor
productivity in eastern Germany is lower than in western Germany. A relatively low marginal labor productivity (MPL) in eastern Germany implies
ceteris paribus relatively high marginal costs in eastern Germany. This
affects the price index Equation (30 ). Moreover, relatively high marginal
costs imply adverse competitiveness for the eastern German firms, which
needs to be corrected by relatively low nominal wages in eastern Germany.
This affects the wage Equation (2). By incorporating the MPL-gap, the wage
Equation (2) and the simplified price index Equation (3’) change into (see
Appendix B)19
"
#1=e
R
D 1e e1
MPLwest ð1eÞ=e X
0
rs
ð2 Þ
Wr ¼ constant Ys T
Is
MPLr
s¼1
00
ð3 Þ
" #1=ð1eÞ
MPLwest 1e
Drcenter 1e
þ ð1 lr Þ WT
Ir ¼ lr Wr
MPLr
18
For each district r the weighted average distance to the other districts s weights Drs is
calculated using weights ¼ Ys/jYj. The district with the smallest average distance is the economic
center.
19
Under the assumptions that there is a uniform level of MPL in western Germany
(MPLwest), which is higher than the uniform level of MPL in eastern Germany; see Appendix B
for the derivation of (20 ) and (300 ).
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BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 457
Equation (300 ) is finally substituted into (20 ), which gives the reduced form
of the equilibrium wage equation without invoking real wage equalization in
order to approximate (3). The equation to be estimated is:
"
#
R
X
1e
logðWr Þ ¼ k0 þ e1 log
ð700 Þ
Ys T Drs
Ise1 þ k1 EG
s¼1
where
h
1e i
Ir1e ¼ lr ðWr ð1 þ gr ÞÞ1e þð1 lr Þ WT Drcenter
; 1 þ gr ek1 EGðrÞe=e1 ; gr
represents the productivity gap between western Germany and district r,
which is (MPLwest/MPLr) 1, and EG(r) is a dummy variable which equals 1
if r is in eastern Germany.
An additional advantage of Equation (700 ) compared to the basic wage
Equation (7) is that the share of income spent on manufactures d (which we
thus found to be rather large in our initial estimation in Table 3) does not need
to be estimated now because the equilibrium condition for the market for
housing services, Equation (5), is no longer needed to estimate the wage
equation.
Table 4 shows the regression results of estimating Equation (700 ).20 The
results for Equation (700 ) in Table 4 show that the distance parameter is now
significantly positive and the same holds for e. In this case—see Equation
(700 )—the results support the notion that nominal wages in district r are
higher if this region has a better access (in terms of distance) to larger
markets. That is to say, our alternative estimation strategy does yield a
spatial wage structure for Germany.21
The estimation results in Table 4 for Germany provide support for the
Helpman-Hanson model in the sense that the model parameters are found to
be significant. Our estimations of wage Equation (700 ) illustrate that Wr is
higher if district r is situated more closely to regions with a relatively high
Y. To some extent this is a surprising result. Certainly compared to the case of
the United States, the German labor market is considered to be rigid, which
could imply in terms of our model that, for whatever institutional reason,
20
We also captured the possibility of no real wage equalization in a more simple way by
sticking to wage Equation (7) and by allowing only for a real wage differential between on the one
hand western and on the other hand eastern German regions by changing Equation (6) into
W
W
s
r
d ¼ P1d I d jrs , where jrs ¼ f > 1, if r is West and s is East, and jrs ¼ 1/f < 1, if r is East and s
P1d
r Ir
s
s
is West. f represents the real-wage gap between East and West Germany (incomplete real-wage
equalization). It turned out that f ¼ 1.406 (t-value 4.768) thereby validating that real wages are
higher in western German regions.
21
As a verification on the validity of the results in Table 3 we calculated Moran’s correlation
coefficient to check for spatial dependencies (and to test for possible mis-specification). It turns out
that, using the residuals from the estimation of Equation (70 ), that there is no spatial dependency.
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TABLE 4: No Real Wage Equalization
Equation (7’’), with EG dummy
3.652 (23.4)
0.003 (13.7)
e
Log(T)
District Specific Control Variables (dummies)
EG
Drural
Industry
Other services
High-skilled
Adjusted R2
0.633
.056
1.052
1.983
5.456
0.99
(16.2)
(1.4)
(5.8)
(5.4)
(11.7)
Estimation method for Equation (700 ): WLS; number of observations: 151; district-specific
control variables that are not statistically significant are omitted; result for the dummy for the
city of Erlangen is not reported, t-statistic in parentheses.
interregional wages are set at the same level.22 For a country like Germany
one might expect that the spatial distribution of Y does not only get reflected
in spatial wage differences but (also) in the spatial distribution of quantity
variables like regional (un)employment (see also Puga, 2002, pp. 389–390,
for this assertion for Germany).23 The proper approach to deal with the
implications of wage rigidity is to incorporate the implications of wage
rigidity, most notably unemployment, into the model and then to
(re)estimate the structural parameters. This is left for future research. Here,
we refer only to Brakman, Garretsen, and Schramm (2002a) where using the
rather crude wage rigidity assumption Wr ¼ Ws (which we have shown in this
section not to be the case, recall also Figure 2!), an employment equation is
derived. Estimation results confirm the existence of a spatial employment
structure.24
Returning to the estimation results in Table 4 and following Hanson
(1998, 2001a), we illustrate the strength of the interregional demand linkages
22
One might expect that the massive transfers between western and eastern Germany are
also an important institutional feature to take into account. We checked for this by using personal
income (which includes transfers) instead of GDP as a measure for the variable Y. Also, we
included the ratio of each district’s GDP to personal income as an additional explanatory
variable in Equation (7). However, this had virtually no impact on the estimation results for the
key model parameters.
23
Interregional wage differences are for instance not feasible if a union ensures centralized
wage setting that is, irrespective of regional economic conditions, Wr ¼ Ws (see Faini, 1999).
Centralized wage setting (at the industry level) is a tenet of the German labor market.
24
Based on a simple market potential function like Equation (1), Brakman, Garretsen, and
Schramm (2002a) test for a spatial employment as well as an unemployment structure and they
find confirmation for the former but, also due to data limitations, not for the latter. Peeters and
Garretsen (2004) show how unemployment can be incorporated into a basic new economic
geography model.
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BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 459
rate of growth of hourly wage
1.0
0.8
0.6
0.4
0.2
0.0
0
200
400
600
time of travel by car from Munich (measured in minutes)
FIGURE 4: Wage growth (%) and Distance, Following a 10 Percent Increase
of GDP in Munich.
Source: Author calculations.
that give rise to the spatial wage structure through the following experiment.
Based on the estimated coefficients in Table 4 we derive the impact on regional wages from a 10 percent GDP increase in the city-district of Munich. The
localization of demand linkages turns out to be quite strong. The positive GDP
shock leads to an increase of wages in Munich itself by 0.8 percent and the
impact on wages in other regions strongly decays with distance. In Berlin, for
instance, the impact is a mere 0.08 percent. This is in line with the findings of
Hanson (2001a) for the United States and Roos (2001) for Germany. Figure 4
shows the results of our ‘‘Munich experiment’’ for each of the German districts.
It clearly shows that the impact of the GDP shock on wages rapidly declines
the further one moves away from Munich.
6.
TWO SIMPLE ALTERNATIVE MODELS FOR A SPATIAL WAGE
STRUCTURE
So far, the estimation results provide some support for the HelpmanHanson model once we no longer have to assume real wage equalization.
Even though our main aim is to estimate and not test this model, our results
in Table 4 raise the question of how well this model specification performs
against alternative models that also include the possibility of a spatial wage
structure. In this section we therefore briefly compare the estimated wage
Equation (700 ) with two simple alternative models, a market potential function
and a wage curve. The market potential function encompasses a wide range of
theoretical approaches and as such represents a summary of alternative
explanations (see Harrigan, 2001). Equation (1) is an example of a market
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JOURNAL OF REGIONAL SCIENCE, VOL. 44, NO. 3, 2004
potential function and here we use the same specification, but now with wages
as the dependent variable—see Equation (10 )
ð10 Þ
logðWr Þ ¼ k1 log
hX
i
k2 Drs
Y
e
þ k3 EG þ k4 Drural þ constant
s
s
where Wr ¼ wages in district r, Yr ¼ income in district r, Drs ¼ distance
between districts r and s, and EG and Drural are two dummies for eastern
German and rural districts, respectively.
The wage curve—see Equation (8)—states that regional wage differences
reflect regional differences in GDP or unemployment but it does not include
geography in the sense that distance between regions is not used as an
explanatory variable (Blanchflower and Oswald, 1994)
ð8Þ
logðWr Þ ¼ b1 logðyr Þ þ b2 logðUr Þ þ constant
where Wr ¼ wages in district r, yr ¼ GDP per capita in district r, and
Ur ¼ unemployment rate in district r.
We proceed as follows. We first estimate the market potential function (10 )
and the wage curve (8) with the same variables controlling for location-specific
effects as used in specification (700 ) and we then compare the models. Table 5
TABLE 5: Alternative Models
Market Potential Equation (10 )
(3.5)
(2.0)
(8.778)
(3.1)
–
–
District Specific Control Variables (dummies)
EG
.654 (9.8)
.126 (3.1)
Drural
Industry
.787 (3.8)
Other services
1.150 (3.0)
Low-skilled
.924 (2.0)
High-skilled
4.823 (9.2)
0.99
Adjusted R2
Akaike information criterion (AIC)
0.989
0.931
AIC for eq. (700 ), with simplified
price index (reduced form)
k1
k2
k3
k4
b1
b2
0.049
0.092
0.655
0.126
Wage Curve (8)
–
–
–
–
0.104 (2.4)
0.002 (0.4)
.653 (8.7)
–
.905 (4.7)
1.641 (4.4)
1.025 (2.0)
4.979 (9.0)
0.99
0.947
No. observations ¼ 151, estimation method: weighted least squares (WLS), result for constant
not reported, result for dummy for the city of Erlangen (80 ) is not reported, t-statistic in
parentheses. District-specific control variables that are not statistically significant are omitted.
Results for Akaike info criterion are based on non linear least squares (NLS) estimations, this
criterion requires that the dependent variables are the same which is not the case with WLS.
# Blackwell Publishing, Inc. 2004.
BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 461
gives the estimation results for Equations (10 ) and (8) and also gives the
Akaike information criterion (AIC) which is used for model selection.
Both the market potential function and the wage curve give the expected
results and thus also give rise to a spatial wage structure. The parameters are
significant and have the expected signs. A low value for the AIC test statistic
is preferred over a higher one. According to this criterion it seems that the
market potential function (10 ) must be slightly preferred over the wage curve
(8) and our wage Equation (700 ).25 We, however, prefer the structural model
over the market potential function or a wage curve, because of its direct link to
theory, and because it allows us to estimate the structural variables. Moreover, the findings seem plausible for the German case. The market potential
approach is in fact a reduced form with no clear link to theory, whereas the
wage curve does not include a spatial structure. More research is clearly
needed here, but for now we must conclude that from an empirical point of
view the choice is more difficult.
7.
CONCLUSIONS
The recent advances in the field of new economic geography have
increased our understanding of spreading and agglomerating forces in an
economy. Empirical testing, however, is difficult. Not only because the core
models are characterized by multiple equilibria, but also because the lack of
specific regional data makes shortcuts inevitable. In this paper we have tried
to find evidence whether or not new economic geography models are in principle able to describe the spatial characteristics of an economy, in this case,
Germany. Using data for German districts we use the so-called HelpmanHanson model to investigate the existence of a spatial wage structure and to
estimate the key model parameters.
We modify and extend the work by Hanson (1998, 2001a) in two ways.
First, in order to deal with housing market we not only use data on the
housing stock but also on land prices. Subsequently, and more importantly,
we drop the assumption of real wage equalization. It is only when we no longer
have to assume that real wages are not equalized across reunified Germany
that we find clear-cut evidence for both a spatial wage structure and the
relevance of structural model parameters. A first brief comparison of our
preferred model specification with two alternative explanations suggests
that the new economic geography approach is a serious alternative to other
explanations of the spatial distribution of wages. A straightforward next step
is to analyze the development of a spatial wage structure over time using a
new economic geography approach and to look at other European countries
besides Germany. In doing so, a major challenge will be to take into account
25
Using a similar test, the Schwarz-criterion, Hanson (2001a) finds for the case of the
United States that wage Equation (7), estimated in first differences, has always to be preferred
compared to the market potential function.
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JOURNAL OF REGIONAL SCIENCE, VOL. 44, NO. 3, 2004
that many European countries are characterized by various forms of wage
rigidity.
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APPENDIX A
DERIVATION OF THE SPATIAL WAGE EQUATION (2)
First look at the demand side of the Helpman (1998) model. Assume an
economy with two sectors, Housing (H) and Manufacturing (M). Every consumer in the economy shares the same Cobb-Douglas preferences for both
types of commodities
U ¼ M d H ð1dÞ
The parameter d is the share of income spent on manufactured goods. Where
M is a CES subutility function of many varieties
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JOURNAL OF REGIONAL SCIENCE, VOL. 44, NO. 3, 2004
M¼
n
X
!1=r
cri
i¼1
Maximizing the subutility subject to the income constraint gives the demand
for each variety j
e1
cj ¼ pe
dY
j I
where I ¼ ½
P
i
1
ðpi Þð1eÞ 1=ð1eÞ is the price index for manufacures, e ¼ 1r
the
elasticity of substitution, and Y ¼ income.
Next, turn to the supply side. Each variety i is produced according to
li ¼ a þ bxi
where li is the amount of labor necessary to produce xi of variety i. The
coefficients a and b describe, respectively, the fixed and marginal labor
requirement. Maximizing profits gives the familiar mark-up pricing rule
1
pi ð1 Þ ¼ wi b
e
Using the zero-profit condition and the mark-up pricing rule above gives the
break-even supply of a variety i (each variety is produced by a single firm)
xi ¼
aðe 1Þ
b
Furthermore, transportation of manufactures is costly. Transportation costs
are so-called iceberg transportation costs, T ¼ TD12 > 1, where D12 is the distance between region 1 and 2. Also assume, for illustration purposes, that
there only two regions, 1, and 2. Total demand for a product from, for example
region 1, now comes from two regions, 1 and 2. The consumers in region 2
have to pay transportation costs on their imports. This leads to the following
total demand for a variety produced in region 1
e1
D12 e e1
x1 ¼ dðY1 pe
þ Y2 pe
Þ I2 Þ
1 I1
1 ðT
We already know that the break-even supply equals x1 ¼ aðe1Þ
b ; equating this
to total demand gives (note that the demand from region 2 is multiplied
by TD12 in order to compensate for the part that melts away during transportation)
aðe 1Þ
e1
D12 1e e1
¼ dðY1 pe
þ Y2 pe
Þ I2 Þ
1 I1
1 ðT
b
Inserting the mark-up pricing rule in this last equation and solving for the
wage rate gives the two-region version of the equilibrium wage Equation (2) in
# Blackwell Publishing, Inc. 2004.
BRAKMAN, GARRETSEN AND SCHRAMM: THE SPATIAL DISTRIBUTION OF WAGES 465
the main text. Also, inserting the mark-up pricing rule into the price index
above gives this index in terms of the wage rate as in Equation (3) in the main
text.
APPENDIX B
DERIVATION OF THE REDUCED-FORM WAGE EQUATION (700 ) WITH A
MARGINAL LABOR PRODUCTIVITY (MPL) GAP BETWEEN EASTERN
AND WESTERN GERMANY
Assume a productivity gap between eastern and western Germany
Lir ¼ a þ ð1 þ gir Þbxir
where Lir is employment in firm i in region r, x is output, gir measures the
marginal labor productivity gap between western Germany and a firm i in
region r and is equal to (MPLwest/MPLir) 1.
Assume a uniform level of MPL in western Germany, and a uniform level
of MPL in eastern Germany: for any firm i in region r in western Germany
MPLir ¼ MPLwest, and for any firm i in region r in eastern Germany
west
MPLir ¼ MPLeast ¼ MPL
1þg ; so gir ¼ 0 if region r is in western Germany, and
gir ¼ g > 0, if region r is in eastern Germany.
Free entry and exit and using the zero-profit condition leads to the
equilibrium output for firm i in region r (see Brakman, Garretsen, and van
Marrewijk, 2001, pp. 78–79)
xir ¼
aðe 1Þ
ð1 þ gir Þb
The equilibrium demand facing each firm i in standard monopolistic competition is
xd ¼
pe
dY
I ð1eÞ
e
ð1 þ gr ÞbW,
Summing over all firms, using the mark-up pricing rule p ¼ e1
and taking iceberg transport costs into account gives
"
#
e
R
X
e Wr T Drs ðbð1 þ gr ÞÞ
Drs Ys
xr ¼
T d
e1
Is
Is
s¼1
where T is transport costs, and Drs is the distance between regions r and s,
and I is the price index of manufactures.
This expression is equal to the break-even supply of each firm
"
1e #
R
e
e X
a:ðe 1Þ
T Drs
Wr ðbð1 þ gr ÞÞ
¼d
Ys
e1
ð1 þ gr Þb
Is
s¼1
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The wage rate in region r is determined by solving this equation for the wage
rate, yielding
"
1e X
1e #
R
bd
T Drs
1e=e e 1
Ys
W r ¼ ð 1 þ gr Þ
eb
ðe 1Þa s¼1
Is
The log transformation of this expression results in the log transformation of
wage Equation (20 )
"
#
R
X
D 1e e1
1e
1
rs
logð1 þ gr Þ þ log
logðWr Þ ¼ constant þ
Ys T
Is
e
e
s¼1
where
1e
<0
e
The productivity gap between western and eastern Germany also affects the
price index Equation (30 ) because marginal cost changes into
MCir ¼ Wir bð1 þ gir Þ
and so, dropping subscript i, the simplified price index Equation (30 ) becomes
h
1e i1=ð1eÞ
Ir ¼ lr ðWr ð1 þ gr ÞÞ1e þð1 lr Þ WT Drcenter
# Blackwell Publishing, Inc. 2004.